Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.

Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa's results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa's (1999) results, and the applicable scope of water depth is deeper.

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

Second-order solutions for random interfacial waves under steady uniform currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Higher order response of nonlinear composite in external AC electric field

The fifth-order effective nonlinear responses at fundament frequency and higher-order harmonics are given for nonlinear composites, which obey a current-field relation of the form J = sigmaE + x\E\(2) E, if a sinusoidal alternating current (AC) external field with finite frequency omega is applied. As two examples, we have investigated the cylinder and spherical inclusion embedded in a host and, for larger volume fraction, also derived the formulae of effective nonlinear responses at higher-order harmonics by the aid of the general effective response definition. Furthermore, the relationships between effective nonlinear responses at harmonics are given. (C) 2003 Elsevier Science B.V. All rights reserved.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

基板预热对激光金属沉积成形过程热应力的影响

为降低沉积过程的热应力,抑制成形过程中裂缝的产生,研究基板预热对激光金属沉积成形(Laser metal deposition shaping,LMDS)过程热应力的影响具有非常重要的意义。根据有限元分析中的"单元生死"思想,利用APDL(ANSYS parametric design language)编程建立多道多层激光金属沉积成形过程的数值模拟模型,深入探讨基板未预热和预热到400℃时对成形过程热应力的影响。计算结果表明,基板预热到400℃可以显著降低成形过程中试样的热应力变化波动性,试样的Von Mises热应力最大值可降低10%左右,其中x方向热应力最大值可降低8.5%左右,z方向热应力最大值可降低8.1%左右。在与模拟过程相同的条件下,利用自行研制的激光金属沉积成形设备进行了成形试验,成形试验的结果与模拟结果基本吻合。

北京市中学生考试焦虑状况及其相关因素分析

In order to analyze the test anxiety of Beijing's high school students, relevant factors affecting test anxiety and how those factors have effect on the test anxiety of those high school students, a cross-sectional study had been conducted among 2,089 students randomly selected from 15 high schools in Beijing, using the Test Anxiety Scale（TAS）, Parenting Style Scale (PSS) and Academic Aggregate Graphic (AAG). Five months later, 194 students from one of those high schools were retested with TAS with students remaining anonymous. In the retest, the classes and birth dates of those students were strictly matched. This paper is composed of three parts to examine the issue. The first part examines the test anxiety among high school students in Beijing and establishes the model; the second part conducts a comparative study of issues related to test anxiety and academic performance; the third part examines the factors affecting test anxiety and establishes the model. Results showed that: 1. The reliability and validity of TAS are satisfied and can meet survey requirement. The 25-item version of TAS turned out to have equal or even better performance compared with the original 37-item version. 2. Incidence of test anxiety in high schools of Beijing: 57.9 percent of samples have an overall score at or higher 15. 55 percent of male student samples have a score at or higher than 15 while that for female student samples is 61 percent. A score of 20 refers to fairly serious test anxiety and 31.9 percent of samples have a score over 20. 28.1 percent of the male student samples have a score of over 20 while that for female student samples is 35.9 percent. 3. The effect of grade and sex and the interaction between the two factors are statistically significant. Female students have higher test anxiety than male students and the level of test anxiety varies from grade to grade. 4. Samples are divided into two groups, one with test anxiety and the other without. The academic performance gap between the two groups is very significant. There is a significant negative correlation between academic score and test anxiety. 5. There is a negative correlation between test anxiety and mastery goal orientation and a positive correlation between test anxiety and performance goal orientation. Students with higher academic self-efficiency have lower test anxiety. The more one thinks study is valuable, the lower his/her test anxiety is. Those whose parents communicate smoothly with them have lower test anxiety. Those whose parents have an inconsistent communication style have higher test anxiety. 6. Achievement goal is mediate variable for the effect of lack of values on test anxiety. 7. The indirect effect of introduction of achievement goal and parenting style, including communication, monitoring and communication consistence, on test anxiety is significant. Key words: Test anxiety，reliability, validity, self-efficiency，parenting style，achievement goal orientation, academic values, academic score